In a letter to The Daily Telegraph, she says that under his leadership Conservatives would be hopelessly split or deeply cynical, "either openly rebelling against him or going along with policies they knew to be wrong".

Lady Thatcher's intervention follows Mr Clarke's admission that, if he were to win the leadership, he would not vote with the rest of his party against the Bill ratifying the Treaty of Nice when the Commons returns in October.

Mr Duncan Smith seized on the statement as evidence that Mr Clarke's views on Europe would make it impossible for him to provide the party with proper leadership.

Yesterday, as ballot papers were sent to more than 300,000 party members, the two candidates published their manifestos.

Mr Duncan Smith's said that he was the only person who could unite the party on Europe, while Mr Clarke presented himself as the man who could win the next election.

Lady Thatcher says that Mr Clarke, a former chancellor, should take responsibility for the party's dire condition.

"It would have been reassuring to hear from Ken Clarke about some mistakes which led the party to the greatest defeat in its history," she writes.

"After all, he, not Iain Duncan Smith, was one of those who made them.

"Indeed, I simply do not understand how Ken could lead today's Conservative Party to anything other than disaster. He is at odds with the majority of its members on too many issues.

"He appears an even keener enthusiast for the euro than is the Prime Minister, let alone the Chancellor. He seems to view with blithe unconcern the erosion of Britain's sovereignty in Europe."

Lady Thatcher praises Mr Duncan Smith as a man who knows that the party cannot regain its standing by aping or outflanking Labour.

Referring to his rebellion over the Maastricht Treaty, she says: "While Mr Duncan Smith is criticised for lacking ministerial experience, it should be remembered that he does so only because he put his integrity before his ambition."

Mr Clarke's attempt to show that he would not force Tories to change their views on Europe backfired. He said that, if he were leader, he would allow the party to carry on opposing the Treaty of Nice Bill in the Commons - then made it clear that he would not vote against it.

"It may well be that my diary will make it difficult for me to be there," he told a news conference at Westminster. "The treaty will then be history. We might as well put it in the bag."

Mr Duncan Smith responded: "My view is clear - when the Nice vote comes, if I am leader I will lead from the front. We will oppose the Nice Treaty, as we have been doing."

David Maclean, MP for Penrith and the Border and a member of Mr Duncan Smith's campaign team, said that Mr Clarke's comments highlighted the folly of his leadership bid.

"This will blow up in our faces on the very first day back as most of the Tories march through the No lobby and our newly-elected leader, to whom we are looking for inspired leadership, would be abstaining. It is an absurd position."

Mr Clarke compared his record of abstaining in European votes when he did not agree with the party line with Mr Duncan Smith's opposition to Maastricht under John Major.

"I did not ever, personally, vote with the Labour Party," he said.

Suggesting that he would be happy for some Eurosceptics to leave the party if he became leader, he said: "I think the Conservative Party has had quite enough of people throwing their toys out of their pram.

"Anybody from either wing of the party who says they are going to leave if they don't like the leader is free to go, because that particular instinct is the kind of thing that has been undermining the party for 10 years."

He said that Mr Maude and Michael Portillo, the failed leadership contender who also promoted the cause of modernisation, would be offered places on the four policy commissions that he would set up if he won.

Mr Clarke described himself as a "social liberal". But he said he would not be distracted by the kinds of issues that derailed Mr Portillo's campaign and that he was opposed to homosexual marriages and the legalisation of cannabis.

Mr Duncan Smith demonstrated his commitment to broadening the appeal of the party by touring the Manningham area of Bradford, the scene of riots last month.

"Conservatives do not represent constituencies in areas like this any more," he said. "We have to find out why, because there are people here who share our values."

But officials said she felt entitled to speak out now as so many others were expressing their opinions.

Her backing for Mr Duncan Smith comes as no surprise. In 1997 she backed William Hague when he was up against Mr Clarke in the final ballot of the contest, but she did not criticise the former chancellor then in the way that she does today.

In her memoirs, The Downing Street Years, she described Mr Clarke, who served in her Cabinet, as a man who would be better inside the Cabinet only "because he would cause more trouble outside".